We develop two schemes for tuning the scattering length on the ground triplet state of Cs2. First, an absolute value of the triplet scattering length of 133Cs2 is determined using the experimental data (Fioretti et al, Eur.Phys.J. 5, 389 (1999)). We demonstrate that the large scattering length can be made small and positive by coupling of the 3Σ + u (6S +6S) potential to the 3Πg state by strong off-resonant radiation. A weaker laser field coupling the 3Σ + u (6S + 6S) continuum to the lowest bound level of the excited 3Σ + g (6S + 6P) also leads to a small positive scattering length. In addition, the scattering length of the 135Cs isotope is found to be positive. The method used solves the Schrödinger equation for two electronic states coupled by an electromagnetic field with approximations employed. The scattering length is determined from calculated continuum wavefunctions of low energy. 1 A positive scattering length is a crucial ingredient in obtaining Bose-Einstein condensation from a gas of ultra-cold atoms. This parameter controls the long range repulsion
Tuning the scattering length on the ground triplet state of Cs2
We develop two schemes for tuning the scattering length on the ground triplet state of Cs2. First, an absolute value of the triplet scattering length of 133Cs2 is determined using the experimental data (Fioretti et al, Eur.Phys.J. 5, 389 (1999)). We demonstrate that the large scattering length can be made small and positive by coupling of the 3Σ + u (6S +6S) potential to the 3Πg state by strong off-resonant radiation. A weaker laser field coupling the 3Σ + u (6S + 6S) continuum to the lowest bound level of the excited 3Σ + g (6S + 6P) also leads to a small positive scattering length. In addition, the scattering length of the 135Cs isotope is found to be positive. The method used solves the Schrödinger equation for two electronic states coupled by an electromagnetic field with approximations employed. The scattering length is determined from calculated continuum wavefunctions of low energy. 1 A positive scattering length is a crucial ingredient in obtaining Bose-Einstein condensation from a gas of ultra-cold atoms. This parameter controls the long range repulsion
Two schemes for tuning the scattering length on the ground triplet state of Cs2 are developed. The absolute value of the triplet scattering length of 133Cs2 is determined from the experimental data [A. Fioretti, D. Comparat, C. Drag, C. Amiot, O. Dulieu, F. Masnou-Seeuws, and P. Pillet, Eur. Phys. J. D 5, 389 (1999)], we demonstrate that the large scattering length can be made small and positive by coupling the 3Σu+(6S+6S) potential to the 3Πg state by strong off-resonant radiation. A weaker laser field coupling the 3Σu+(6S+6S) continuum to the lowest bound level of the excited 3Σg+(6S+6P) state also leads to a small positive scattering length. The scattering length of the 135Cs isotope is found to be positive. The method used solves the Schrödinger equation for two electronic states coupled by an electromagnetic field with no approximations employed. The scattering length is determined from the calculated continuum wave functions at low energies.
The Morse/Long Range (MLR) potential has become one of the most reliable and highly \nused potential energy functions for diatomic molecules. It includes the theoretical long range \nbehaviour that diatomic molecules are known to exhibit as they approach the dissociation \nlimit. Heavy alkali metals with adjacent electronic states often exhibit strong coupling \nbetween the spin and orbital angular momentum. The ground state X¹Σg⁺ and the lowest \nlying triplet state aᶟΣᵤ⁺ of Cs₂ exhibit such coupling effects and as a result, modeling the \nhighest vibrational states of these states is a non-trivial problem. Utilizing scattering length \nvalues obtained from published analysis of 60 Feshbach resonances, the correct form of the \npotential energy function was determined. Moreover, the scattering length values were used \nto determine the correct leading dispersion coefficient that describes the true form of the \nlong-range potential energy functions. All previous attempts to determine global potential \nenergy functions for these states have considered only the optical spectroscopic data. This is \nthe first ever effort attempting to use scattering lengths determined from cold atom collision \nexperiments in a combined analysis with conventional spectroscopic data.
We use double-resonance photoassociative spectroscopy of ultracold 39K atoms to precisely determine the triplet $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ scattering length for the various isotopes of potassium. Photoassociation of free 39K atoms to the pure long-range ${0}_{g}^{\ensuremath{-}}{(v}^{\ensuremath{'}}=0,{J}^{\ensuremath{'}}=2)$ level is followed by stimulated emission to high-lying levels of the $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ potential. The binding energies of levels within 5 GHz below the lowest ground-state 4s1/2(fa=1)+4s1/2(fb=1) hyperfine asymptote are measured by both trap loss and ionization detection. The locations of these near-threshold hyperfine-coupled molecular levels allow us to constrain the triplet potential and thereby determine the triplet scattering length. The result for 39K, ${a}_{t}=\ensuremath{-}33\ifmmode\pm\else\textpm\fi{}{5a}_{0}$ (1a0=0.0529177nm), is a factor of $\ensuremath{\sim}5$ improvement over previous determinations and establishes that a large 39K Bose-Einstein condensate will not be stable.
The stochastic variational method is used in conjunction with stabilization ideas to compute the low-energy s-wave phase shifts and scattering lengths for Ps-Ps scattering. The scattering lengths obtained were 8.44a0 for the singlet-singlet and 3.00a0 for the triplet-triplet states (the spin state refers to the coupling of the two electrons and the coupling of the two positrons in the system). The positive scattering length in the triplet-triplet channel means a stable Bose-Einstein condensate of triplet Ps atoms is physically possible. The large value of the ${}^{3}{\mathrm{Ps}}^{3}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{Ps}}}^{1}{\mathrm{Ps}}^{1}\mathrm{Ps}$ cross section, $7.41\ensuremath{\pi}{a}_{0}^{2}$ suggests the use of spin-polarized positrons as advanced by Platzmann and Mills [Phys. Rev. B 49 454 (1994)].
Ultralong-range Cs 2 Rydberg-ground molecules ( nD 5/2 + 6 S 1/2 F ) (33 ≤ n ≤ 39, F = 3 or 4) are investigated by a two-photon photo-association spectroscopy of an ultracold Cs gas. Two vibrational ground molecular spectra of triplet 3 Σ and hyperfine mixed singlet-triplet 1,3 Σ molecular states and their corresponding binding energies are attained. The experimental observations are simulated by an effective Hamiltonian including low energy electron scattering pseudopotentials, the spin-orbit interaction of the Rydberg atom, and the hyperfine interaction of the ground-state atom. The zero-energy singlet and triplet s-wave scattering lengths are extracted by comparing the experimental observations and calculations. Dependences of the measured binding energies on the effective principal quantum number, n eff = n − δ D ( δ D is the quantum defect of Rydberg D state), yield the scaling of n eff − 5.60 ± 0.16 ( 3 Σ , F = 3 ) , n eff − 5.62 ± 0.16 ( 3 Σ , F = 4 ) for deep triplet potential and n eff − 5.65 ± 0.38 ( 1 , 3 Σ , F = 3 ) , n eff − 6.19 ± 0.14 ( 1 , 3 Σ , F = 4 ) for shallow mixed singlet-triplet potential well. The simulations of low-energy Rydberg electron scattering show agreement well with the experimental measurements.
We observe the formation of long-range Cs2 Rydberg molecules consisting of a Rydberg and a ground-state atom by photoassociation spectroscopy in an ultracold Cs gas near 6s1/2(F=3,4)→np3/2 resonances (n=26-34). The spectra reveal two types of molecular states recently predicted by D. A. Anderson, S. A. Miller, and G. Raithel [Phys. Rev. A 90, 062518 (2014)]: states bound purely by triplet s-wave scattering with binding energies ranging from 400 MHz at n=26 to 80 MHz at n=34, and states bound by mixed singlet-triplet s-wave scattering with smaller and F-dependent binding energies. The experimental observations are accounted for by an effective Hamiltonian including s-wave scattering pseudopotentials, the hyperfine interaction of the ground-state atom, and the spin-orbit interaction of the Rydberg atom. The analysis enables the characterization of the role of singlet scattering in the formation of long-range Rydberg molecules and the determination of an effective singlet s-wave scattering length for low-energy-electron-Cs collisions.